A conventional box end 100 is shown in FIG. 10 and generally includes twelve ridges 101 and grooves 102 defined in an inner periphery of the box end 100. The ridges 101 and the grooves 102 are arranged in alternative arrangement with each other so that a hexagonal shaped nut 103 can be received in the box end 100 and each peak portion 1030 of the nut 103 is received in one of the grooves 102 and each side 1031 is in contact with the ridges 101. Nevertheless, it is noted that the width “W1” of the width of each ridge 101 is smaller than the width “W” of the opening between the adjacent ridges 101. The width “W1” is smaller than a width of the base of each ridge 101, and the width “W” of the opening is smaller than a width of the bottom of the groove 102. There will be gaps defined between the two adjacent ridges 101 and each peak portion 1030 because the width “W” such that one of two adjacent sides 1031 is not in contact with the ridge 101. In other words, the peak portions 1030 are not well clamped by the ridges 101 and the box end 100 has to be rotated an angle to let the ridges 101 touch the sides 1031 of the nut 103 to rotate the nut 103. This could break the peak portions 1030 because the peak portions 1030 are not clamped firmly.
The present invention intends to provide a polygonal member engaging device whose ridges and grooves are shaped and sized so that the nut can be snugly matched and clamped.